Asymptotic Properties of the Conditional Hazard Function and its Maximum Estimation under Right-Censoring and Left-Truncation

Abstract

Gneyou[6, 7] considered the estimation of the maximum hazard rate under random censorship with covariate random and established strong representation and strong uniform consistency with rate of the estimate. Then he studied the asymptotic normality of his estimator. Agbokou et al.[2] generalize this work to the case of right censored and left truncated data with covariate and established strong representation and strong uniform consistency with rate of the estimate of the said estimator and of a non-parametric estimator of its maximum value. The aim of this paper is to study the asymptotic normality result of the two non-parametric estimators.

Key words and phrases. Conditional hazard rate, maximum conditional hazard rate, non-parametric estimation, kernel, right censoring, left truncation, asymptotic normality.

1991 Mathematics Subject Classification. 62N01, 62N02, 62P10, 62P12